We can sometimes make better predictions with a small number of principal components in Z than a much larger number of variables in X. Success requires that we make a good choice of the number of components. To illustrate the use of PCR and the other shrinkage methods in this chapter, we will use a set of data where the emphasis is on prediction but the explanatory aspects of the methods can be useful in gaining intuition about the structure of the data. A Tecator Infratec Food and Feed Analyzer working in the wavelength range of 850 to 1050 nm by the near-infrared transmission (NIT) principle was used to collect data on samples of finely chopped pure meat and 215 samples were measured. For each sample, the fat content was measured along with a 100-channel spectrum of absorbances. Since determining the fat content via analytical chemistry is time consuming, we would like to build a model to predict the fat content of new samples using the 100 absorbances which can be measured more easily. See Thodberg (1993) for more details.